The Wiener measure is (in the classical sense) a Gaussian measure on the Banach space $C[0,1]:=\{f:[0,1] \to \mathbb{R} \mid f\text{ is continuous and } f(0)=1\}$.

The Wiener process is a stochastic process whose definition can be found in any textbook. In any text, the stochastic integrals or stochastic differential equations use the notation $dW$ frequently, which should denote the Wiener measure, I suppose.

However, I cannot figure out the exact relation between the Wiener 'process' and 'measure'. Wikipedia says that the Wiener process induces the Wiener measure but what exactly does that mean?

I am afraid this question might not belong to MO but I ask here. Could anyone please clarify and help me understand?